# Maximum a posteriori estimation through simulated annealing for binary asteroid orbit determination

## TL;DR

This paper introduces a Bayesian MAP estimation method using simulated annealing for binary asteroid orbit determination, effectively handling uncertain initial conditions and non-Gaussian observational errors.

## Contribution

It presents a novel combination of Bayesian modeling with simulated annealing for robust global optimization in asteroid orbit determination.

## Key findings

- Validated with simulated data showing accurate orbit estimation.
- Successfully applied to real asteroid data confirming effectiveness.
- Guarantees convergence to the global optimum regardless of initial estimates.

## Abstract

This paper considers a new method for the binary asteroid orbit determination problem. The method is based on the Bayesian approach with a global optimisation algorithm. The orbital parameters to be determined are modelled through an a posteriori distribution made of a priori and likelihood terms. The first term constrains the parameters space and it allows the introduction of available knowledge about the orbit. The second term is based on given observations and it allows us to use and compare different observational error models. Once the a posteriori model is built, the estimator of the orbital parameters is computed using a global optimisation procedure: the simulated annealing algorithm. The maximum a posteriori (MAP) techniques are verified using simulated and real data. The obtained results validate the proposed method. The new approach guarantees independence of the initial parameters estimation and theoretical convergence towards the global optimisation solution. It is particularly useful in these situations, whenever a good initial orbit estimation is difficult to get, whenever observations are not well-sampled, and whenever the statistical behaviour of the observational errors cannot be stated Gaussian like.